Best Known (104, 104+92, s)-Nets in Base 4
(104, 104+92, 130)-Net over F4 — Constructive and digital
Digital (104, 196, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 98, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(104, 104+92, 172)-Net over F4 — Digital
Digital (104, 196, 172)-net over F4, using
(104, 104+92, 2167)-Net in Base 4 — Upper bound on s
There is no (104, 196, 2168)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10212 257115 414645 905615 852642 586257 861738 197251 069113 090261 001937 461888 475184 838542 691531 487754 980808 452216 692044 740870 > 4196 [i]